Colander are location aware entities that collaborate to determine
approximate location of mobile or static objects when beacons from an object
are received by all colanders that are within its distance R. This model,
referred to as arrangement-based localization, does not require distance
estimation between entities, which has been shown to be highly erroneous in
practice. Colander are applicable in localization in sensor networks and
tracking of mobile objects.
A set S⊂R2 is an (R,ϵ)-colander if by placing
receivers at the points of S, a wireless device with transmission radius R
can be localized to within a circle of radius ϵ. We present tight
upper and lower bounds on the size of (R,ϵ)-colanders. We measure the
expected size of colanders that will form (R,ϵ)-colanders if they
distributed uniformly over the plane